The inspection of public infrastructure, such as viaducts and bridges, is crucial for their proper maintenance given the heavy use of many of them. Current inspection techniques are very costly and manual, requiring highly qualified personnel and involving many risks. This article presents a novel solution for the detailed inspection of viaducts using aerial robotic platforms. The system provides a highly automated visual inspection platform that does not rely on GPS and could even fly underneath the infrastructure. Unlike commercially available solutions, our system automatically references the inspection to a global coordinate system usable throughout the lifespan of the infrastructure. In addition, the system includes another aerial platform with a robotic arm to make contact inspections of detected defects, thus providing information that cannot be obtained only with images. Both aerial robotic platforms feature flexibility in the choice of camera or contact measurement sensors as the situation requires. The system was validated by performing inspection flights on real viaducts.